powerPA2 {factorial2x2}

Power of the Proportional Allocation 2 procedure

Description

Computes the Proportional Allocation 2 procedure's power to detect the overall A effect or the simple AB effect, respectively.

Usage

powerPA2(n, hrA, hrB, hrAB, avgprob, probAB_C, critPA2A, critPA2ab, dig)

Arguments

n

total subjects with n/4 subjects in each of the C, A, B, and AB groups

hrA

group A to group C hazard ratio; hrA < 1 corresponds to group A superiority

hrB

group B to group C hazard ratio; hrA < 1 corresponds to group A superiority

hrAB

group AB to group C hazard ratio; hrAB < 1 corresponds to group AB superiority

avgprob

event probability averaged across the C, A, B, and AB groups

probAB_C

event probability averaged across the AB and C groups

critPA2A

rejection critical value for the overall A stratified logrank statistic

critPA2ab

rejection critical value for the simple AB ordinary logrank statistic

dig

number of decimal places to which we roundDown the critical value for the overall A test as calculated in powerPA2 by strLgrkPower

Details

The Proportional Allocation 2 procedure uses a two-sided 2/3 * alpha significance level to test the overall A effect and the remaining Dunnett-corrected type 1 error to thest the simple AB effect. When the familywise error is alpha = 0.05, this corresponds to a critical value critPA2A = -2.13. Then crit2x2 is used to compute a critical value critPA2ab = -2.24 to test the simple AB effect. This corresponds to a two-sided 0.0251 significance level. This controls the asymptotic familywise type I error for the two hypothesis tests at the two-sided 0.05 level. This is because of the 1/sqrt(2) asymptotic correlation between the logrank test statistics for the overall A and simple AB effects (Slud, 1994). The overall A effect's significance level 2/3 * 0.05 is prespecified and the simple AB effect's significance level 0.0251 is computed using crit2x2.

Value

powerPA2overallA

power to detect the overall A effect

powerPA2simpleAB

power to detect the simple AB effect

Author(s)

Eric Leifer, James Troendle

References

Leifer, E.S., Troendle, J.F., Kolecki, A., Follmann, D. Joint testing of overall and simple effect for the two-by-two factorial design. (2020). Submitted.

Lin, D-Y., Gong, J., Gallo, P., et al. Simultaneous inference on treatment effects in survival studies with factorial designs. Biometrics. 2016; 72: 1078-1085.

Slud, E.V. Analysis of factorial survival experiments. Biometrics. 1994; 50: 25-38.

See Also

crit2x2, eventProb, lgrkPower, strLgrkPower

Examples

 # Corresponds to scenario 4 in Table 2 from Leifer, Troendle, et al. (2020).
 rateC <- 0.0445  # one-year C group event rate
 hrA <- 0.80
 hrB <- 0.80
 hrAB <- 0.72
 mincens <- 4.0
 maxcens <- 8.4
 evtprob <- eventProb(rateC, hrA, hrB, hrAB, mincens, maxcens)
 avgprob <- evtprob$avgprob
 probAB_C <- evtprob$probAB_C
 dig <- 2
 alpha <- 0.05
 corAa  <- 1/sqrt(2)
 corAab <- 1/sqrt(2)
 coraab <- 1/2
 critvals <- crit2x2(corAa, corAab, coraab, dig, alpha)
 critPA2A <- critvals$critPA2A
 critPA2ab <- critvals$critPA2ab
 n <- 4600
 powerPA2(n, hrA, hrB, hrAB, avgprob, probAB_C,
            critPA2A, critPA2ab, dig)
# $powerPA2overallA
# [1] 0.6582819

# $powerPA2simpleAB
# [1] 0.9197286